Photonic crystals are the optical analogues of semiconductors. In a semiconductor, the electronic bandgap arises as a result of a periodic array of electronic potentials defined by the material and its crystalline structure. In a photonic crystal, the photonic bandgap arises as a result of a structured periodic variation in refractive index of two or more dielectric materials. Optical waves and frequencies lying within this forbidden bandgap cannot propagate through the photonic crystal without severe attenuation. In particular, three-dimensional (3-D) photonic crystals exhibit omnidirectional reflection of incident waves for all directions and polarizations within the bandgap. The average wavelength of the photonic bandgap is approximately twice the lattice constant of the photonic crystal structure. Feature sizes associated with photonic crystals are on the order of one-eighth the wavelength of light. These considerations suggest that these artificial photonic crystals can be engineered to have specific photonic properties by controlling the dimensions and materials comprising the lattice.
Just as semiconductors revolutionized electronics, it is expected that photonic crystals will revolutionize optical computing and communications. However, the field of photonic crystals is in its infancy. Development of photonic crystals has been hampered because the production of high quality photonic crystals currently requires expensive, complex fabrications schemes. To replace conventional optical materials for integrated optical applications, a simple, low-cost manufacturing process is needed for producing 3-D photonic crystals and embedding several other optical components onto a single chip.
Yablonovitch and John were the first to suggest a 3-D photonic crystal for optical applications. See E. Yablonovitch and T. J. Gmitter, Phys. Rev. Lett. 63, 1950 (1989); and S. John, Phys. Rev. Lett. 58, 2486 (1987). Yablonovitch proposed that a slanted-pore structure (“Yablonovite”) comprising two widely different indexes of refraction could be created by drilling periodic cylindrical holes with a diameter of between 0.1 and 0.2 of the desired wavelength into a slab at three different angular orientations. See E. Yablonovitch, J. Opt. Soc. Am. 10, 283 (1993). The 3-D periodicity of the Yablonovite structure produced a photonic band gap to all angles of incident light with wavelengths approximately twice the lattice spacing.
Deep X-ray lithography (DXRL) can be used to fabricate the 3-D Yablonovite structure. DXRL uses X-rays generated by a synchrotron light source to pattern thick photoresist. X-rays emitted from the light source are highly collimated and capable of patterning photoresist, such as polymethyl methacrylate (PMMA), with critical dimensions of less than 1 μm and aspect ratios significantly greater than 10:1. To fabricate Yablonovite with DXRL, an X-ray mask is needed that consists of a hexagonal array of round holes. This mask is mounted in near-proximity to the surface of a thick layer of photoresist. It is then exposed three times using collimated X-rays arriving from an elevation angle of 53° and from three azimuth angles: 0°, 120°, and 240°. See E. Yablonovitch and K. M. Leung, Physica B 175 (1-3), 81 (1991). The Yablonovite structure has been successfully fabricated in PMMA by several researchers. See G. Feiertag et al., Appl. Phys. Lett. 71(11), 1441 (1997); C. Cuisin et al., Optical and Quantum Electronics 34, 13 (2002); and F. Romanato et al., Microelectronic Engineering 67-68, 479 (2003).
However, because there are circular holes in the Yablonovite-structure mask and the X-rays pass through the holes at a significant angle, ellipses are patterned into the photoresist. X-ray masks are typically 5- to 8-μm-thick, so at the 37° angle of incidence, the X-rays are further vignetted. With this fabrication process, Yablonovite comprising 6-μm features or greater can be made with these thick masks, but these large feature sizes are not particularly useful for mid-IR applications. DXRL masks as thin as 0.7 μm have been used to demonstrate Yablonovite patterns in PMMA with smaller feature sizes. However, line broadening of the exposed PMMA structure could not be eliminated using this thin mask. See F. Romanato et al., J. Vacuum Science and Tech. B 21(6), 2912 (2003).
Further, the mask/resist combination must be exposed three separate times to create the Yablonovite structure. Where the holes in the structure overlap one-another, the X-ray dose is a factor-of-3 greater than where the holes are not overlapped. Also, the X-ray beams are attenuated through the thickness of the thick photoresist—preferably by a factor-of-5 to minimize beam time and not overexpose the top surface. Therefore, the X-ray flux in the exposed resist can vary by as much as a factor-of-15. Gas can be generated in the overexposed areas due to resist degradation, producing internal stress in the pattern that can damage the unexposed regions of the polymer resist. See J. Mohr et al., Macromolecular Chemistry: Macromolecular Symposium 24, 231 (1989).
Finally, X-rays that reach the substrate and plating base can be absorbed at the resist/substrate interface. The X-rays can produce secondary emissions, some of which radiate back into the photoresist and expose the bottom portion of the resist. See A. Ting, Journal of Microlithography, Microfabrication, and Microsystems 3(3), 413 (2004). Therefore, the bottom of the structure can be severely damaged and attachment of the photoresist to the substrate can be greatly weakened. This weakness can be a significant problem because the photoresist expands during the development. Therefore a contiguous structure, such as the mold for Yablonovite, tries to grow relative to the unexposed photoresist surrounding it. This growth creates large compressive stresses in the photoresist. These stresses are relieved when the structure detaches itself from the substrate.
As a result of these fabrication difficulties, the Yablonovite structure has limited utility for practical applications. Further, to date, no one has been able to plate metal or other high index material into a template mold made of the developed photoresist.
In the late 1990's, researchers at Iowa State University developed a model design for producing a wider 3-D bandgap using a logpile (or woodpile) structure. This logpile structure is equivalent to a face-centered-cubic crystal when the fill fraction is near 28%. See K. Ho et al., Solid State Comm. 89, 413 (1994); and H. S. Sozuer and J. P. Dowling, J. Modern Optics 41, 231 (1994). The logpile structure can be fabricated using traditional lithographic patterning techniques to create 3-D photonic crystals for both visible and infrared applications. This logpile structure was first fabricated in silicon by Lin et al. using a surface micromachining method, wherein the layers of logs are built up sequentially, to provide a wide bandgap at wavelengths from 8 to 14 μm. See S.-Y. Lin et al. Phys. Rev. B 59, 579 (1999); and U.S. Pat. No. 6,869,330 to Gee et al.
In FIG. 1 is shown a perspective-view schematic illustration of the logpile structure 10 that can be fabricated on a substrate 14 using the surface micromachining method of Lin et al. The 3-D logpile structure comprises alternating layers 27′, 27, 29′, and 29, each layer comprising an evenly spaced row of parallel “logs” or rods 12 of a dielectric material (e.g., silicon or tungsten). The rods have a width of w. The spaces 13 between the rods 12 can be filled with air (as shown) or a second dielectric material. For a four-layer photonic crystal 10, the one-dimensional rods 12 have a stacking sequence that repeats itself every four layers with a repeat distance of c. Within each layer 27′, 27, 29′, or 29, the axes of the rods 12 are parallel to each other with a pitch of d. Alternate layers are rotated by 90 degrees relative to the previous layer. Between each alternating parallel layer 27 and 29, or 27′ and 29′, the rods are shifted relative to each other by 0.5 d. The resulting structure 10 has a face-centered-tetragonal lattice symmetry of which the diamond structure is a subset.
For the special case of c/d=1.414, the crystal 10 can be derived from a face-centered-cubic unit cell with a basis of two rods.
Logpile structures of both silicon and tungsten have been fabricated by Lin et al. For the tungsten photonic crystal, the tungsten rods were approximately w=1.2 μm wide and spaced at a pitch of d=4.2 μm, thereby providing a band edge at λ=5 μm. Unfortunately, fabrication of this logpile structure by surface micromachining is difficult. The vertical topology of the 3-D logpile structure is built up, layer-by-layer, by repetitive deposition and etching of multiple dielectric films, requiring multiple aligned lithographic patterning steps. To simplify the fabrication of logpile photonic crystals, Toader et al. developed a method to fabricate a tilted logpile structure that required only two lithographic exposures and only one repositioning of the mask between exposures. See O. Toader et al., Phys. Rev. Lett. 90(23), 233901 (2003); and O. Toader et al., Phys. Rev. E. 71, 036605 (2005). In FIG. 2B is shown a side-view schematic illustration of Toader's tilted logpile structure 20 patterned in a thick layer of photoresist 23 on a substrate 24 after the two exposures. The tilted logpile 20 has the same lattice structure as Lin's conventional logpile 10, but the tilted logpile 20 is simply rotated with respect to the substrate 24 by 90 degrees out-of-plane and 45 degrees in-plane to orient the <001> direction parallel to the substrate 24, rather than normal to the substrate 14 (i.e., for the tilted logpile 20, the <110> direction is normal to the plane of the substrate 24 and the <001> direction is into the plane of FIG. 2B).
In FIG. 2A is shown a top-view schematic illustration of a portion of Toader's mask 25 comprising a pattern of openings 26 and 28 in an X-ray-absorbing material 22 on a transparent membrane substrate (this mask portion will pattern four layers in the <001> direction—an actual mask would comprise an array of mask openings to pattern a 3-D photonic crystal comprising a plurality of unit cells). Toader's method uses two exposures and a single mask repositioning between exposures to fabricate the tilted logpile structure 20 (exemplary exposures through a single representative mask opening 26 or repositioned mask opening 26′ are shown in FIGS. 2A-2C).
As shown in FIG. 2B, the mask 25 is mounted in near-proximity to the surface of the photoresist 23. A first exposure, with the incident radiation 21 tilted at a +45 degree angle with respect to the mask normal N and aligned with the mask openings, patterns the first half of the logpile structure 20 into the resist 23. The first exposure therefore patterns a layer of rods 27 through mask openings 26 and a layer of rods 29 through mask openings 28 parallel to the <010> lattice direction. The mask 25 is then repositioned on the photoresist 23 by one-half the distance to the pattern's nearest neighbor. The second exposure is then performed with incident beam 21′, also at a 45 degree tilt angle but after rotating the repositioned mask 25 and substrate 24 by 180 degrees, to pattern the other half of the logpile structure 20 into the resist 23. This rotation is equivalent to performing the second exposure with the incident beam 21′ at a −45 degree tilt angle with respect to the mask normal N without the mask/substrate rotation. The second exposure therefore patterns layers of rods 27′ and 29′ parallel to the <100> lattice direction through the repositioned mask openings 26′ and 28′, respectively.
In FIG. 2C is shown an end-view schematic illustration of Toader's tilted logpile structure. The patterned rods 27, 27′, 29, and 29′ in adjacent layers are parallel to each other and non-overlapping.
When using a positive photoresist with this mask pattern, development of the patterned resist produces an inverse tilted logpile structure comprising layers of holes in the developed resist. Therefore, Toader further suggested that the developed photoresist could be used as a template mold to fabricate a tilted logpile structure of metallized rods using a LIGA process. LIGA is the German acronym for a MEMS processes utilizing deep X-ray Lithography, Galvanoforming, and Abformung (injection molding) to create plastic, metal, and ceramic microparts with very high aspect ratios and critical dimensions ranging from a few microns to a few centimeters. The first step of the LIGA process is to use DXRL to pattern thick photoresist. The exposure is commonly performed using a metallized substrate with resist either spin coated or laminated over the metallized surface. The patterned photoresist is then developed in a liquid solvent to remove the exposed low molecular weight polymeric materials (i.e., with a positive resist) leaving the unexposed material defined by X-ray exposure. The second step in the LIGA process uses electroplating to deposit metal into the developed high-aspect-ratio pattern. Subsequent removal of the remaining photoresist results in a free standing metal structure. Using a similar LIGA process, a tilted logpile structure can also be fabricated using metal, plastic, ceramic, or glass to fill an inverse tilted logpile mold.
Toader's tilted-logpile fabrication method is much simpler than the layer-by-layer logpile fabrication method of Lin et al. In addition, the overall X-ray dose required to fabricate the tilted logpile is reduced compared to that required to fabricate Yablonovite, since only two exposures are necessary. Further, because the exposed regions do not overlap, the dose does not have the factor-of-3 variation between the overlapped and non-overlapped regions found in the Yablonovite fabrication method.
Unfortunately, hardware requirements for submicron translation and alignment of a DXRL mask to a substrate between exposures have prevented the production of large-area, high-quality tilted logpile photonic crystals using Toader's method. Therefore, a need remains for a simple method to fabricate large-area, high-quality tilted logpile photonic crystals.